Search Documents

By David Green

Outokumpu introduced Flash Flotation in the early l 980's for the recovery of floatable material from grinding circuits. The devel­opment came as a result of surveys made in the company's own concentrators, initiated to find ways of improving recoveries with increasingly complex and lower grade feeds. Hydrocyclones make a separation on the basis of particle size and mass, resulting in the "over collection" of fine grained, high S.G. particles. Minerals such as pentlandite, galena and gold are easily caught in the circulating load around the mill until they are overground and rendered more difficult to collect. In the case of downstream flotation this may simply involve a reduction in the rate coefficient due to the finer sizes or, as is commonly experienced in gold operations, the mate­rial is slimed and coated onto non-floating gangue and is eventual­ly lost to tails. At the time of Outokumpu's plant surveys, it was a relatively common practice, particularly in Pb operations, to have a flotation section fed directly from the secondaiy mill discharge. This is called unit flotation and certainly provided an improvement but very high wear rates and frequent sanding out of the cells was com­mon. The development of the SkimAir® Flash Flotation cell by Outokumpu provided a subtle but quite dramatic departure from the unit cell approach. Now it was possible to feed cyclone under­flow into a special purpose-built flotation machine and recover a final grade concentrate from the grinding circuit (see Figure I). The cell was designed to handle the coarse circulating load, per­mitting the coarsest fractions to be short-circuited back to the mill and retain the floatable sizes for a nominal time of 30 seconds to several minutes. The short retention time was possible largely due to the relatively clean content of the cyclone underflow stream. This means that the fine gangue is not present except in small quan­tities and most of the fine to mid-size paiiicles are higher S.G. and more likely represent valuable mineral. This condition provides for very high rate coefficients. Typical operations would recover 40-60% of the valuable mineral in this fashion and improvements in recovery were typically from 2-5% for sulphide minerals to the 5-20% range for gold and silver.

Jan 1, 1998

By S. K. Kawatra

Three International Symposiums-the 14th International Minerals Processing Congress, the 17th APCOM, and the SME-AIME Fall Meeting special symposium on Design and Installation of Com¬minution Circuits-held in 1982 contained a number of papers relating to the fundamentals of processing coals and metallic minerals. In addition, many papers were published elsewhere in the literature. Some of the more significant papers are discussed below. Flavel reviewed key performance parameters, such as energy-size relationships for crushing processes and presented a fundamental basis for optimizing crusher productivity and possibly for development of improved crushers. Pascoe et al. reviewed the use of such control schemes. Magerowski and Karra presented a paper on a computer program developed to and in the design of crushing circuits. The problems associated with the scale-up to very large ball mills were discussed by Arbiter and Harris, and by Kavetsky and Whiten. Both groups concluded that limits on mill productivity arise due to problems associated with particle breakage and transport through mills. Austin et al., and Herbst and Rajamini reviewed the state of the art for the use of grinding circuit simulators for design and control. The effects of mill operating and design parameters on selection and breakage were discussed in detail. The philosophy of control and instrumentation for grinding circuits was extensively discussed by Kawatra and Seitz. Their paper presented for the first time an analytical basis for the inferential particle sizing technique and provided a fundamental basis for the implementation of this technique. The effect of reagent addition variation's on the performance of coal flotation circuits was reported by Kawatra and Waters, and on sulfide flotation circuits by Klimpel et al. Both groups analyzed circuit behavior from a kinetic point of view and reached similar conclusions on the effects of collectors and frothers. The computer simulation of an iron ore flotation circuit also was reported by Kawatra et al. In this work particular attention was paid to the phenomena of froth overloading. Klimpel et al., Kawatra and Waters, and Niemi et al. discussed the philosophy of control by flotation circuits from a fundamental kinetic point of view. An extension of the use of high intensity magnetic separators to the beneficiation of specular hematite was discussed by Thayer and Linkson.

Jan 5, 1983

By D. W. Scott, D. G. Minnes

Introduction Ontario's diverse industrial mineral resource base includes structural minerals such as sand and gravel, crushed stone, building stone, clay, shale, limestone, and dolostone. These resources are used to produce aggregates, brick, metallurgical stone, fillers, cement, lime, and other construction materials. The majority of the operations are in deposits of Palezoic and Quaternary age in southern Ontario, close to the major markets. Province-wide, there were more than 140 Mt (154 million st) of aggregates produced in 1985. About 115 Mt (128 million st) of that was produced in southern Ontario with the rest being largely from Crown land in northern Ontario. Structural industrial minerals account for more than 80% of the value of total industrial mineral production. The remaining 20% is accounted for by the nonstructural minerals, such as salt, which is produced in the southwestern part of the province. A host of other nonstructural industrial minerals are known. Production, though, is currently restricted to calcite, gypsum, quartz, talc, nepheline syenite, and byproduct metallurgical sulfur products (Fig. 1). Major production is close to the large markets of urbanized southern Ontario and the northeastern and northcentral US. With an abundant variety of industrial mineral resources and the large population within 650 km (400 miles) of most deposits, the market offers great potential. Ontario's nine million people accounted for about 35% of Canada's entire $476.3 billion gross domestic product in 1985. This equates to about one-third of the nation's buying power being within a 200-km (125-mile) radius of Toronto. This major concentration of industrial and economic activity has resulted in a well-developed industrial minerals industry that fulfills most of the structural industrial minerals demand in Ontario. Nonstructural industrial minerals are similarly well placed to compete in this high demand area. Although Ontario manufacturers still import some of these materials, Ontario products are achieving significant market share. And, they serve the needs of neighboring provinces and states. Present production and trends Ontario has traditionally produced significant amounts of industrial minerals. This produc¬tion had a value of $956 million in 1984 (Table 1). Structural materials production in 1985 and 1986 approached or exceeded levels not seen since the early 1970s. Many new products have been developed using these raw materials. The industry is becoming concentrated in the hands of several large companies, mainly four large cement com-

Jan 12, 1987

By D. Bahrami, G. Danko, W. Asante

"It is prudent to interpret atmospheric monitoring signals in real-time for checking the safe limits of the air conditions in underground mines. In gassy mines, such real-time evaluation increases the safety of operation. In all mines, the continuous monitoring and evaluation contribute to maintaining air conditions to be within healthy and safe limits. Signal interpretation for safety conditions in mines is difficult for many reasons. An increase of hazardous contaminant concentrations can be predicted by signal pattern recognition, root-cause analysis of rapid changes toward deterioration and forward prediction in time using algorithms and numerical models. This paper focuses on analyzing signal patterns to recognize dangerous trends as well as forward predicting the various environmental and working conditions that may affect safety in underground mines. Efficient numerical ventilation model with heat and gas contaminant simulation components is needed for the analysis of real-time atmospheric monitoring data. Computational speed enhancement methods are discussed and tested in numerical examples, using the Jacobian sensitivity matrices for signal propagation prediction. INTRODUCTION The focus area of this paper is mine safety, related to hazardous atmospheric conditions in a mine ventilation system. Improvements by recognizing safety hazards caused by heat of combustible gases or the accumulation of poisonous gases in a mine are addressed. The recognition of safety hazard by manual evaluation is difficult because of the complex nature of information and the large amount of monitored data from measurement by atmospheric sensors such as air velocity, pressure, hazardous gas contaminants and temperature. In order to recognize problem-causing trends, it is necessary to evaluate continuously individual measurement data from the Atmospheric Monitoring System (AMS) of the mine during their time-dependent variations. In addition, the combined effects of various signal trends need to be simultaneously interpreted in their cross-effects. It is very difficult to foresee the possible outcomes of intertwined signatures of various problems by continuous human observation. For example, a steady, continuous methane concentration measurement together with a sharp drop in barometric pressure from the AMS sensors may be a case for worry in future time due to pressure-induced methane increase from the coal seam or the gob (Danko et al., 2013). This future increase can be predicted by a time-dependent Ventilation Air Model (VAM) and its surrogate Air Parameter Predictor Solver (APPS) model. A calibrated VAM or APPS model can indeed predict a likely methane concentration variation in future time as a function of previous and new air pressure as well as air velocity (Danko, et. al., 2013). Such a future trend, however, cannot be seen from the raw measurement data."

Jan 1, 2017

By III Westbrook

Although calcium sulfate dihydrate, commonly referred to as gypsum, has been utilized for some time in fiberglass reinforced polyester (FRP) applications, it does not have the fire retardant filler recognition of ATH. Gypsum is more commonly known for application in cement, soil and water treatment, plaster, and wall-board. Inherent characteristics of gypsum limit its use to low temperature and, until recently, non-aqueous applications. However, as a plentiful, naturally occurring hydrated mineral, the cost effectiveness of calcium sulfate dihydrate has prompted development and yielded success in the areas of FRP spray-up and latex carpet backing.

Jan 1, 1993

By Stephen P. Mulqueen

Searles Lake is an evaporite basin located near the community of Trona in northwestern San Bernardino County, CA. Searles Valley Minerals Operations Inc. (SVM), a subsidiary of Nirma Limited, currently manufactures more than 1.58 Mt/a (1.75 million stpy) of industrial minerals from natural brines produced from several lakebeds within the basin. The chemical manufacturing facilities in Searles Valley represent extremely complex operations involving solution mining and mineral extraction processes.

Jan 1, 2012

By Thomas Novak, Sampurna Arya

Controlling dust generation and keeping it below permissible limits to meet federal dust standards at the working face of a room-and-pillar coal mine is a challenge for a mine operator. With the recent changes in federal dust regulations requiring lower worker exposure, maintaining compliance has become increasingly difficult. The current most effective practice of dust control at a continuous miner face in an underground mine is the use of a flooded-bed scrubber. A study carried out by the U.S National Institute for Occupational Safety and Health (NIOSH) indicated that a flooded-bed scrubber could achieve cleaning efficiencies between 58 and 90 percent. But the operation of such a system is maintenance intensive. The flooded-bed scrubber screen becomes clogged with dust particles and requires frequent cleaning to maintain performance. However, the dust control issue is not solely a mining-industry problem. Other industries face similar issues. The University of Kentucky collaborated with Toyota Motor Manufacturing on the development of a novel wet scrubber, called the vortecone scrubber, for capturing over-sprayed paint particles in automotive paint booths. The vortecone scrubber achieved a cleaning efficiency of 99 percent and required minimal maintenance. This study aims to assess the ability of this vortecone scrubber to capture respirable dust in an underground coal mine. The paper presents the results of computational fluid dynamics (CFD) modeling of this vortecone scrubber. It discusses the effects of air quantity and dust particle size on the performance of the scrubber. 

By M. A. Trevits, G. Frampton

"Mine safety training materials have long included pictures of mine conditions, equipment, hazards, etc. These images are invaluable to both the trainee and the trainer to convey many important concepts. The human eye takes in a tremendous amount of information, while the field-of-view from a consumer grade camera is, generally, 40 degrees to 90-degrees. This difference in field-of-view is a primary reason that pictures, especially of dark and dusty areas, don’t adequately describe the scene. For conveying information to a trainee, these images lack context. Today, 360-degree cameras are available with consumer-grade cameras costing a few hundred dollars. Also, the display technology is already owned by most trainees and trainers and is widely available. The resulting 360-degree videos and pictures can be readily viewed on smart phones and inserted into Microsoft PowerPoint slideshows. These images and videos can easily be included in existing training modules, disseminated using the internet, and used by trainees easily. We propose a methodology for utilization of 360-degree video and images with simple display technology for miner training. INTRODUCTION AND BACKGROUND In mining, as in other production-related industries, the safety of workers is dependent upon many interrelated factors. One of the more important safety factors is a miner's ability to recognize hazards in their workplace. The ability to perceive and identify hazards is perhaps more difficult to master in underground mining than in general industry because the work environment is confined, noisy, dark, and inherently dangerous because of the hidden unknowns created by the geological setting and the conditions created by the mine opening. Further complicating the situation is a setting that is continuously changing as mining advances (Barrett 1995) [1]. Hours of excellent mine safety training have been developed and utilized over the years. Pictures of mines, activities, hazards, etc., are included in many of these training courses. These photographs, especially those taken underground, often lack context because of the limitations of the cameras and lenses. Notable research by the US Bureau of Mines and then later by NIOSH showed that the use of stereoscopic three-dimensional slides in training exercises was an effective aid for improving the ability of miners to recognize hazardous ground control conditions (Barrett 1988) [2]. An example of type of three-dimensional slides and slide viewer is shown in figure 1."

Jan 1, 2018

By J. A. Ehler

Speed and torque control of standard A.C. induction motors can be accomplished using a variety of devices ranging from mechanical, hydraulic, and electrical. Also, the motor can be specified as an A.C. wound rotor or D.C. motor using the associated controls. Normally, any one of these drive types can be adequately used to provide the torque control necessary to accelerate a conveyor belt system. The selection will depend on the economics, experience, and preference of the designer or end user. These drive types will be presented from a functional and performance viewpoint to assist in the understanding of the available technology.

Jan 1, 1998

By Arthur P. Chase

The Tacubaya subway tunnels form a link in the Sistema de Transporte Colectivo (Mass Transit System) of the Federal District of Mexico. One tunnel 327 m long lies to the north of Tacubaya Station, the other 811 m long, to the south. The tunnels are designed to accommodate two subway trains, one inbound and one outbound, within the inside diameter of 8.5 m. The designers of the tunnel lining and tunnel driving equipment were faced with the problem of driving two subway tunnels 9.0 m outside diameter through water-bearing soil, directly beneath a high speed limited access highway, a main drainage sewer, structures including residences and office buildings, on an alignment curved for 67 per cent of tunnel length, and on grades as high as 7 per cent, within a limited budget, with minimum damage to property and disruption to the community. Planning The following decisions affecting tunnel design and construction were made at an early stage of planning: Shield. To enhance safety, a tunnel shield would be used for tunnel driving. Dewatering. The water-bearing soil could be effectively dewatered; consequently, tunnel driving could be performed in free air. Hand Mining. To minimize investment in equipment, hand mining would be used to excavate and support the face.

Jan 1, 1997

By David F. Gibson

This paper presents an outline of several models that have been developed to aid surface mine planners evaluate alternative mining methods and dragline sizes. The models presented belong to a larger group of models that are incorporated in the SEAMPLAN computerized mine and reclamation planning system. SEAMPLAN was developed in the College of Engineering at Montana State University. Initial funding for the development was derived from the USDA Forest Ser- vice and EPA. Enhancements to SEAMPLAN are currently being funded by DOE (Contract DE-AC22-80ET-14173). SEAMPLAN is a comprehensive surface mine and reclamation planning tool that contains a number of major modules: Data Entry and Review, Production Analysis, Reclamation Analysis, and Impact Analysis. The Production Analysis Module contains programs that enable the user to evaluate alternative methods of removing overburden in a surface coal mine and then to assess auxiliary activities required to support the overburden removal operation. A set of these programs addresses the use of draglines for removing overburden. Six basic dragline mining techniques have been modeled. For one-pass dragline operations four methods can be analyzed: (i) simple side cast, (ii) side bench, (iii) extended bench, and (iv) extended bench with side bench. Two methods of two-pass operations are modeled: (i) single dragline, and (ii) tandem draglines.

Jan 1, 1982

By Jaye Pickarts, Bret Boster, Jack McPartland

Pegasus Minera de Chile, Ltda. is completing three phases of metallurgical evaluation on the Pullalli project to develop a preliminary process flowsheet. A project feasibility study is in progress. The feasibility study includes a proposed process flowsheet designed based on results from the multiple stages of metallurgical evaluation. Phases I and II of metallurgical evaluation included laboratory scale heap leach and milling cyanidation testwork on multiple drill core composites and bulk ore samples from the Pullalli Project. Phase Ill included pilot scale milling/cyanidation testwork on Pullalli drill core composites. The proposed flowsheet includes selective mining and separate processing of low grade and high grade ores. Low grade ore will be crushed and heap leached. High grade ore will be milled leached for 12 hours in an agitated cyanidation circuit. After 12 hours of leaching, sands and slimes will be separated and the sands will be washed using a counter current cyclone (CCC) circuit. Partially leached and washed sands will be added to the crushed low grade ore for heap leaching treatment and permanent placement. Partially leached slimes will be thickened in a high capacity thickener and will be processed in a CIP circuit. Leached slimes will be placed in a tailings impoundment.

Jan 1, 1996

By Norman E. Breslow, John A. Montgomery, Sanford W. Horstman

Reconstruction of historical exposures to silica dust is required in an ongoing cohort mortality study of workers in the diatomaceous earth (DE) industry. However, historical data were collected using three different sampling methods. This study was conducted to derive empirical quantitative relationships from linear regression equations between the three methods: standard impinger, total mass, and respirable mass. Dust from one diatomaceous earth processing plant was sampled simultaneously by all three methods. Results from 61 clusters of the three sampling devices indicate that the phcle size distribution of the dust varies with the two parent products sampled. baghouse product and main product. The relationships between particle counts and respirable mass are: Respirable mass (mg/m3) = 0.064 (mppd) impinger count for baghouse product dust, and respirable mass (mg/m3) = 0.018 (mppcf) impinger count for main product dust. The relationships between particle counts and total mass are: Total mass (mg/m3) = 0.837 (mppcf) impinger count for baghouse product, and total mass (mg/m3) = 1.21 (mppcf) for main product dust. In all four euuations, the intercept did not differ significantly from zero, and the correlation coefficients ranged from 0.90 to 0.95. Results are compared with data from four previously published studies.

Jan 1, 1991

By L. C. de Kooker, K. Esmaeili, I. Musonda, M. Ferentinou

This paper presents the results of an investigation into the effect of pore pressure regime on the factor of safety (FS) and the anticipated critical failure mechanism for a fly ash storage facility. In this study, pore pressure measurements from standpipe piezometers and pore pressure estimated from seepage analysis were used for a comparison of the estimated FS for a fly ash slope. This comparison was applied for static and seismic scenarios. To account for the uncertainties resulting from the limited data available and support a qualitative risk assessment evaluation, a probabilistic analysis was performed. The slope stability analysis was conducted in 2D and 3D, adopting the limit equilibrium analysis approach, and a finite element seepage analysis. The results suggest consistency of failure surfaces for 2D and 3D and an increase in FS values of 5 percent for the 3D approach, limitations of standpipe piezometers. The study demonstrated the sensitivity of the FS value, and the implication of adopting representative material properties, and water table levels, especially in cases where limited data are available, and assumptions need to be made to assess the long-term stability of a fly ash dam facility.

Aug 1, 2024

By S. D. Van Nort

Editor’s note: This is the first of two MINING ENGINEERING articles about the Grasberg deposit. The second, focusing on open pit mine development, will appear in the April issue of the magazine. The Grasberg porphyry copper-gold deposit of Freeport Indonesia Inc. lies within the Ertsberg Mineral District in central Irian Jaya, Indonesia. The Grasberg deposit was discovered during a drilling campaign initiated in the mid-1980s. Production at the open pit de- posit commenced in December 1989. The Grasberg copper-gold ore body is contained within a young igneous complex of dioritic composition that intrudes limestones of the Tertiary New Guinea Group. Alteration is typical of porphyry copper deposits worldwide except that higher grade primary chalcopyrite with significant gold values is associated with a centrally located zone of strong quartz stockwork. Irian Jaya comprises the western half of the island of New Guinea. The Ertsberg District lies 70 km (43 miles) inland from the Arafura Sea at an altitudeof3500 to45OOm (11,480to 14,764 ft). It straddles the Papuan fold belt. This belt forms the east-west trending chain of mountains that extend the entire length of New Guinea and is the site of numerous mineral districts.

Jan 1, 1991

By Odd E. Hanssen

In April 1982, the contracting Companies, ABV of Sweden and Hoyer-Ellefsen of Norway forming the Consorcio Escandinavo Agoyan, signed the contract for the construction of the civil works of the Agoyan Hydroelectric Project, located in Ecuador, South America. The project is located in the Andes mountain region of Ecuador - one of the smaller countries in this part of the world, located on the Pacific Coast. The contract was signed with the Instituto Ecuatoriano de Electrificación (INECEL), a public institution in charge of the development of all major energy producing projects in Ecuador, for a value of approximately US$ 120,000,000. The contract's main elements are - Concrete gravity dam with a total volume of approximately 210,000 cu m. (60 m wide x 45 m maximum height, 320 m crest). - 2,400 m of headrace tunnel, interior diameter of finished lining 6 m of which 450 m is in-situ tunnel formed in a trench. - Pressure shafts, 132 m long, the lowest meters with sheet lining, the rest with concrete lining. - Powerhouse cavern with an excavated volume of approximately 25,000 c m in which two turbines of 78 MW each will be installed. - Two 140 m tailrace tunnels with a finished diameter (concrete

Jan 1, 1985

By A. Ghosh

Commonly used predictors of ground vibration from blasting, being linear in log-log plot, do not model the underlying physics of wave attenuation. Amplitude of the wave decays with distance due to geometrical spreading and inelastic attenuation producing a nonlinear carve in log-log scale. The nolinear decay of seismic waves has also been observed from non-explosive sources, such as, pile driving, drop hammer, traffic, etc. The improved predictors, by explicitly taking these two mechanisms into consideration, model the data trend extremely well at all distance ranges. Actual field data from different studies have been used to validate the improved models.

Jan 1, 1991

By Ray Brainard, Adriana Ventimiglia, Amanda Kerr

Preliminary design is underway for a new Southern Nevada Water Authority (SNWA) project that will ensure one of America’s most reliable water systems by providing continued, reliable water service to existing and future customers. The Horizon Lateral is a $1.6 billion water transmission pipeline that includes 7–10 miles of 108-inch finished diameter rock and soft-ground tunnels. The tunnels will traverse volcanic rock in or around the McCullough Mountain Range and the surrounding alluvial basin. The tunneling community will find relevance in hearing about this critical infrastructure project from a leading wholesale water utility owner with a proven track record for on-time, collaborative projects.

Dec 1, 2022

By R. D. Williams

"In a very real sense, Butte, MT is where the copper came from that won two world wars. The price for that unrestricted mining and smelting of copper came due in 1983 when Butte was declared a Superfund site.One of the most complex remnants of this mining history is the Parrot Tailings site. The Parrot smelter operated from 1881 to 1910, moving Upper Silver Bow Creek to the south and depositing approximately 283,000 m3 (370,000 cu yd) of waste material adjacent to Upper Silver Bow Creek. Additional mixed waste from other processing sites deposited below the Parrot tailings at the Northside Tailings, Diggings East and Blacktail Creek Berm total approximately 171,000 m3 (224,000 cu yd) of contaminated material. As part of the Superfund remedy, the U.S. Environmental Protection Agency (EPA) proposed leaving all these wastes in place. This proposal prompted a detailed criticism by several geoscientists familiar with the site. The EPA’s 2006 Record of Decision (ROD) did in fact leave these wastes in place, which set the stage for a series of studies that continue to refine how best to protect extensive completed Superfund Remediation downstream of Upper Silver Bow Creek. History of the Parrott Mine and tailingsPlacer gold was discovered in Silver Bow Creek, the headwaters of the Clark Fork River only a few miles from the Continental Divide in 1864. This discovery led to a stampede of placer and lode claims. One of the first lode claims located was the Parrot lode, located in the fall of 1864. Progress for developing a mine at the Parrott was slow, and it was not until 1876 that one of the original locators encountered a rich vein of chalcocite. Butte had its first copper mine.The Parrott Mine was patented in 1879 and by 1881 the Parrot, having lost a “t”, concentrator and smelter were built. The smelter and concentrator were an immediate success with a considerable market for processing the district’s rich copper ore. In 1885, the employees of the Parrot smelter bought the Butte Reduction Works, another smelter. In 1885, dams were built on Silver Bow Creek to contain various tailings and related processing byproducts (Fig. 1).By 1890, the various smelters in Butte rendered Butte’s air quality as suffocating (Fig. 2). An 1889 funeral procession was rumored to have gotten lost in the thick smelter smoke and somehow ended up at the Centennial Brewery. A city ordinance was passed late in 1890 in an attempt to control smoke. The Parrot smelter employed approximately 500 men by 1890. Through the 1890s, the tailings produced grew from approximately 91 t/d (100 stpd) to more than 181 t/d (200 stpd). Copper values in the tailings were initially as high as 4 percent, but as the processing improved that was reduced to 1.5 percent."

Apr 1, 2019

By R. J. Pindred

Discussion by R.J. Pindred In his paper, Davis presents an overview of risk. He also introduces the Capital Asset Processing Model (CAPM) as a foundation for selecting the appropriate discount rate for a mining project. While applying portfolio theory is more defensible than the ad hoc adjustment of discount rates, the CAPM is not a panacea. CAPM shortcomings [The CAPM, as Davis stated, is expressed in the equation: ri=rf+pi4) where ri is the project discount rate rf is the risk free interest rate (3i is the project beta, and 0 is the market risk premium (rm - rf)] Application of the CAPM is more difficult than Davis indicates. Valuation is prospective, while the CAPM parameters are historical. Beta is determined from a regression analysis of historical data, while the beta needed for valuation is the expected beta. Betas are known to be unstable and the regressions that generate them often have low explanatory power. The difficulty of estimating a "project" beta must also be considered. Thus, the beta that is used in the CAPM will be based on the analyst's judgment. Like Cavender's discount rate, this judgment can lead to different project NPVs. Subjectivity in valuation cannot be avoided by a mechanical application of the CAPM. The risk-free rate, which Davis identifies as a short-term real rate of 4%, is also subject to scrutiny. A mining project is not a short-term investment and no single risk-free rate is appropriate for all of the cash flows. The hypothetical mine discussed in Cavender's paper is a six-year project. One might argue for the application of a risk-free rate from the Treasury yield curve at the duration of the project (in a bond-duration sense). This, too, is inappropriate. The risk-free rate should be matched to the timing of the cash flow. These rates can be determined by calculating the implied forward rates from the yield curve using a procedure known as "bootstrapping." It is likely that each of the project's cash flows would be discounted at a different rate. Commodity prices Davis criticizes the "ad hoc adjustment to the discount rate." Yet, in his discussion of the value of stochastic simulation, he suggests that the gold price be modeled as a "random walk, with or without a trend." This is essentially an arbitrary modeling of price risk. Consider that a liquid market in gold futures exists. The futures' price curve, which is closely related to the market's estimate of future spot gold prices, should be used to provide inputs to the model. This is especially true of a relatively short six-year project. Alternatively, as Davis correctly points out, a risk-averse investor can sell the commodity short to hedge price risk. Is it any more correct, in the portfolio sense, to account for price risk at all ?? References Cavender, B., 1992, "Determination of the optimum lifetime of a mining project using discounted cash flow and option pricing techniques," Mining Engineering, Vol. 44, No. 10, pp.1262-1268 Fabozzi, F.J., 1993, Bond Markets, Analysis and Strategies, Second Edition, Prentice Hall, Inc. Higgins, R.C., 1992, Analysis for Financial Management, Third Edition, Richard D. Irwin, Inc. Solnik, B., 1991, International Investments, Second Edition, Addison Wesley Reply by G.A. Davis Pindred discusses two issues related to my paper, the shortcomings of the Capital Asset Pricing Model (CAPM) and which commodity price values to use in the valuation exercise. Even though these topics are not directly related to the use or misuse of Monte Carlo simulation, they are important points to take into consideration in valuation exercises. Since I do not appear to have addressed these issues satisfactorily in my original paper, I will comment on each here. Pindred agrees with me that applying portfolio theory, and specifically the CAPM, to the selection of project discount rates is more defensible than ad hoc methods. But he then points out that the application of the CAPM to project valuation is more difficult that I indicate. It is true that the CAPM is a difficult tool for project valuation in general,. But the application of the CAPM to mining projects is one of the easiest I can think of. The biggest problem with using the CAPM for project valuation is coming up with an expected project beta. I suggest a project beta for gold projects of 0.45. The "true" value might be 0.35, 0.55 or whatever. Pindred correctly notes that the selection of the appropriate project beta is based

Jan 1, 1996